A loop \(ABCDEFA\) of straight edges has six corner points \(\mathrm{A}(0,0,0), \mathrm{B}(5,0,0),\)\(\mathrm{C}(5,5,0) ,\mathrm{D}(0,5,0), \mathrm{E}(0,5,5)\) and \(\mathrm{F}(0,0,5) .\) The magnetic field in this region is \(\overrightarrow{\mathrm{B}}=(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}) \;\mathrm{T}\). The quantity of flux through the loop \(\mathrm{ABCDEFA}(\text { in Wb })\) is

A disc is rolling without slipping on a surface. The radius of the disc is \(R\). At \(t=0\), the top most point on the disc is \(A\) as shown in figure. When the disc completes half of its rotation, the displacement of point \(A\) from its initial position is

The bulk modulus of a liquid is \(3 \times 10^{10}\, Nm ^{-2}\). The pressure required to reduce the volume of liquid by \(2 \%\) is  ........ \(\times 10^{8}\; Nm ^{-2}\)

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\((a)\) \({R}_{{H}}\) (Rydberg constant)	\((i)\) \({kg} {m}^{-1} {s}^{-1}\)
\((b)\) \(h\) (Planck's constant)	\((ii)\) \({kg} {m}^{2} {s}^{-1}\)
\((c)\) \(\mu_{{B}}\) (Magnetic field energy density)	\((iii)\) \({m}^{-1}\)
\((d)\) \(\eta\) (coefficient of viscocity)	\((iv)\) \({kg} {m}^{-1} {s}^{-2}\)

Choose the most appropriate answer from the options given below:

For a transistor to act as a switch, it must be operated in

A square loop of side \(10 \mathrm{~cm}\) and resistance \(0.7\  \Omega\) is placed vertically in east-west plane. A uniform magnetic field of \(0.20 \mathrm{~T}\) is set up across the plane in north east direction. The magnetic field is decreased to zero in \(1 \mathrm{~s}\) at a steady rate. Then, magnitude of induced emf is \(\sqrt{\mathrm{x}} \times 10^{-3} \mathrm{~V}\). The value of \(x\) is _______.

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area \(0.5 \mathrm{~m}^2\). It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)\)

In the given figure the magnetic flux through the loop increases according to the relation \(\phi_{B}(t)=10 t^{2}+20 t\), where \(\phi_{B}\) is in milliwebers and \(t\) is in seconds. The magnitude of current through \({R}=2 \,\Omega\) resistor at \({t}=5\, {s}\) is \(....\,{mA}\).

From the given transfer characteristic of a transistor in \(CE\) configuration, the value of power gain of this configuration is \(10^{ x }\), for \(R_B=10\,k \Omega\), and \(R _C=1\,k \Omega\). The value of \(x\) is \(.....\).

\(2\, kg\) of a monoatomic gas is at a pressure of \(4\times10^4\, N/m^2\). The density of the gas is \(8\, kg/m^3\). What is the order of energy of the gas due to its thermal motion ?